User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions

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Added optimal ET sequences
Line 171: Line 171:
* [3, -6, 1, 1⟩ (979:972)
* [3, -6, 1, 1⟩ (979:972)
* [-6, 7, -2, 0⟩ (243:242)
* [-6, 7, -2, 0⟩ (243:242)
{{Optimal ET sequence|legend=1| 7, 17, 24, 41* }}
(* val for 89 is lowered)


=== Example MOS scale: Floor[17] ===
=== Example MOS scale: Floor[17] ===
Line 300: Line 304:
* [-5, 4, -1, -1⟩ (1000:979)
* [-5, 4, -1, -1⟩ (1000:979)
* [-5, -2, -1, 3⟩ (704969:704000)
* [-5, -2, -1, 3⟩ (704969:704000)
{{Optimal ET sequence|legend=1| 5*, 6, 13, 19, 32 }}
(* vals for 55 and 89 are raised)


=== Example MOS scale: Teefs[19] ===
=== Example MOS scale: Teefs[19] ===
Line 481: Line 489:
* [-16, 1, 1, 1⟩ (8277:8192)
* [-16, 1, 1, 1⟩ (8277:8192)
* [-2, 1, 3, -3⟩ (714984:704969)
* [-2, 1, 3, -3⟩ (714984:704969)
{{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129* }}
(* val for 62 is lowered)


=== Example MOS scale: Lylla[19] ===
=== Example MOS scale: Lylla[19] ===
Line 612: Line 624:
* [-6, 3, 0, -1⟩ (729:712)
* [-6, 3, 0, -1⟩ (729:712)
* [-8, 2, 1, -1⟩ (729:712)
* [-8, 2, 1, -1⟩ (729:712)
{{Optimal ET sequence|legend=1| 4*, 5*, 6, 13, 19 }}
(* val for 89 is raised)


=== Example MOS scale: Rocket[19] ===
=== Example MOS scale: Rocket[19] ===

Revision as of 17:41, 13 June 2023

Methodology

These temperaments were documented in honour of the members of Batch 89, as depicted in Guardians of the Galaxy Vol. 3 (2023).

Each of the temperaments tempers four harmonics, representing the eternal friendship and togetherness of their four souls.

Each of the temperaments includes the 2nd harmonic, representing the fact that each of these characters had not one, but two creators: the hands that made them, and the hands that guide the hands.

Each of the temperaments also includes the 89th harmonic, representing their shared trauma and hardship, and how they gave each other the strength to endure and transcend it.

The other two harmonics were selected based on the characters' names. The reason for using their names as a basis, is because choosing their own name was these characters' most symbolic act of asserting their individuality, it was an undeniable demonstration that they had souls capable of creativity. Souls which did not come from, nor belong to, their makers, but which were, and are, their own. Thus, it's fitting that the names they chose should be immortalised in these temperaments:

  • One harmonic was chosen by converting the first letter of the character's name to a number using the A1Z26 cypher, and using that number.
  • The other was chosen by converting each of the letters of the character's name to a number using the A1Z26 cypher, and then summing the numbers together.

Floor (2.6.66.89)

Equal Temperament Mappings

2 6 66 89
[ ⟨ 7 18 42 45 ]
⟨ 17 44 103 110 ] ⟩


Reduced Mapping

2 6 66 89
[ ⟨ 1 2 4 5 ]
⟨ 0 2 7 5 ] ⟩


TE Generator Tunings (cents)

⟨1200.5110, 351.0646]


TE Step Tunings (cents)

⟨34.45745, 56.42993]


TE Tuning Map (cents)

⟨1200.511, 3103.151, 7259.496, 7757.878]


TE Mistunings (cents)

⟨0.511, 1.196, 6.223, -13.002]


Equal Temperament Mappings

2 6 66 89
[ ⟨ 7 18 42 45 ]
⟨ 17 44 103 110 ] ⟩


Reduced Mapping

2 6 66 89
[ ⟨ 1 2 4 5 ]
⟨ 0 2 7 5 ] ⟩


POTE Generator Tunings (cents)

⟨1200.0000, 350.9151]


POTE Step Tunings (cents)

⟨34.44279, 56.40591]


POTE Tuning Map (cents)

⟨1200.000, 3101.830, 7256.406, 7754.576]


POTE Mistunings (cents)

⟨0.000, -0.125, 3.133, -16.304]

Complexity 0.420587
Adjusted Error 7.639353 cents
TE Error 1.179689 cents/octave


Unison Vectors

  • [-3, 1, -1, 1⟩ (89:88)
  • [0, -5, 0, 2⟩ (7921:7776)
  • [3, -6, 1, 1⟩ (979:972)
  • [-6, 7, -2, 0⟩ (243:242)

Optimal ET sequence: 7, 17, 24, 41*

(* val for 89 is lowered)

Example MOS scale: Floor[17]

  • 56.430
  • 147.317
  • 203.747
  • 294.634
  • 351.065
  • 407.495
  • 498.382
  • 554.812
  • 645.699
  • 702.129
  • 793.016
  • 849.446
  • 905.877
  • 996.764
  • 1053.194
  • 1144.081
  • 1200.511

Teefs (2.20.55.89)

Equal Temperament Mappings

2 20 55 89
[ ⟨ 13 56 75 84 ]
⟨ 6 26 35 39 ] ⟩


Reduced Mapping

2 20 55 89
[ ⟨ 1 4 5 6 ]
⟨ 0 2 5 3 ] ⟩


TE Generator Tunings (cents)

⟨1200.8989, 187.8292]


TE Step Tunings (cents)

⟨73.92353, 39.98217]


TE Tuning Map (cents)

⟨1200.899, 5179.254, 6943.641, 7768.881]


TE Mistunings (cents)

⟨0.899, -7.060, 6.009, -1.999]


POTE Generator Tunings (cents)

⟨1200.0000, 187.6886]


POTE Step Tunings (cents)

⟨73.86819, 39.95225]


POTE Tuning Map (cents)

⟨1200.000, 5175.377, 6938.443, 7763.066]


POTE Mistunings (cents)

⟨-0.000, -10.936, 0.812, -7.814]

Complexity 0.305923
Adjusted Error 6.983419 cents
TE Error 1.078398 cents/octave


Unison Vectors

  • [-5, 1, -1, 1⟩ (89:88)
  • [0, 3, 0, -2⟩ (8000:7921)
  • [-5, 4, -1, -1⟩ (1000:979)
  • [-5, -2, -1, 3⟩ (704969:704000)

Optimal ET sequence: 5*, 6, 13, 19, 32

(* vals for 55 and 89 are raised)

Example MOS scale: Teefs[19]

  • 73.924
  • 113.906
  • 187.829
  • 261.753
  • 301.735
  • 375.658
  • 449.582
  • 489.564
  • 563.488
  • 637.411
  • 711.335
  • 751.317
  • 825.241
  • 899.164
  • 939.146
  • 1013.070
  • 1086.993
  • 1126.975
  • 1200.899

Lylla (2.12.62.89)

Equal Temperament Mappings

2 12 62 89
[ ⟨ 19 68 113 123 ]
⟨ 17 61 101 110 ] ⟩


Reduced Mapping

2 12 62 89
[ ⟨ 1 5 5 6 ]
⟨ 0 -3 2 1 ] ⟩


TE Generator Tunings (cents)

⟨1200.8527, 567.7861]


TE Step Tunings (cents)

⟨45.54316, 19.73721]


TE Tuning Map (cents)

⟨1200.853, 4300.905, 7139.836, 7772.902]


TE Mistunings (cents)

⟨0.853, -1.050, -5.200, 2.022]


Equal Temperament Mappings

2 12 62 89
[ ⟨ 19 68 113 123 ]
⟨ 17 61 101 110 ] ⟩


Reduced Mapping

2 12 62 89
[ ⟨ 1 5 5 6 ]
⟨ 0 -3 2 1 ] ⟩


POTE Generator Tunings (cents)

⟨1200.0000, 567.3830]


POTE Step Tunings (cents)

⟨45.51082, 19.72320]


POTE Tuning Map (cents)

⟨1200.000, 4297.851, 7134.766, 7767.383]


POTE Mistunings (cents)

⟨0.000, -4.104, -10.270, -3.497]

Complexity 0.448830
Adjusted Error 4.188048 cents
TE Error 0.646730 cents/octave


Unison Vectors

  • [7, 0, 1, -2⟩ (7936:7921)
  • [-9, 1, 2, -1⟩ (2883:2848)
  • [-16, 1, 1, 1⟩ (8277:8192)
  • [-2, 1, 3, -3⟩ (714984:704969)

Optimal ET sequence: 2, 13, 15, 17, 19, 36, 55, 129*

(* val for 62 is lowered)

Example MOS scale: Lylla[19]

  • 65.281
  • 130.561
  • 195.842
  • 261.122
  • 306.664
  • 371.945
  • 437.225
  • 502.506
  • 567.786
  • 633.067
  • 698.347
  • 763.628
  • 828.908
  • 894.189
  • 939.731
  • 1005.011
  • 1070.292
  • 1135.572
  • 1200.853

Rocket (2.18.72.89)

Equal Temperament Mappings

2 18 72 89
[ ⟨ 6 25 37 39 ]
⟨ 13 54 80 84 ] ⟩


Reduced Mapping

2 18 72 89
[ ⟨ 1 4 6 6 ]
⟨ 0 1 1 3 ] ⟩


TE Generator Tunings (cents)

⟨1201.4486, 190.1507]


TE Step Tunings (cents)

⟨69.06250, 60.54412]


TE Tuning Map (cents)

⟨1201.449, 4995.945, 7398.842, 7779.144]


TE Mistunings (cents)

⟨1.449, -7.965, -5.068, 8.264]


POTE Generator Tunings (cents)

⟨1200.0000, 189.9215]


POTE Step Tunings (cents)

⟨68.97923, 60.47112]


POTE Tuning Map (cents)

⟨1200.000, 4989.921, 7389.921, 7769.764]


POTE Mistunings (cents)

⟨0.000, -13.989, -13.989, -1.116]

Complexity 0.166586
Adjusted Error 9.186573 cents
TE Error 1.418615 cents/octave


Unison Vectors

  • [-2, -1, 1, 0⟩ (1:1)
  • [2, 1, -1, 0⟩ (1:1)
  • [-6, 3, 0, -1⟩ (729:712)
  • [-8, 2, 1, -1⟩ (729:712)

Optimal ET sequence: 4*, 5*, 6, 13, 19

(* val for 89 is raised)

Example MOS scale: Rocket[19]

  • 60.544
  • 129.606
  • 190.151
  • 250.695
  • 319.757
  • 380.301
  • 440.846
  • 509.908
  • 570.452
  • 630.997
  • 691.541
  • 760.603
  • 821.147
  • 881.692
  • 950.754
  • 1011.298
  • 1071.842
  • 1140.904
  • 1201.449
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